Use Euler's method with step size 0.1\displaystyle {0.1} to estimate y(0.5)\displaystyle {y}{\left({0.5}\right)}, where y(x)\displaystyle {y}{\left({x}\right)} is the solution of the initial-value problem
y=3x+y2,   y(0)=1.\displaystyle {y}'={3}{x}+{y}^{{2}},\ \ \ {y}{\left({0}\right)}=-{1}.

y(0.5)=\displaystyle {y}{\left({0.5}\right)}=   .